Problem: Stephanie is 2 times as old as Umaima. 42 years ago, Stephanie was 9 times as old as Umaima. How old is Umaima now?
Solution: We can use the given information to write down two equations that describe the ages of Stephanie and Umaima. Let Stephanie's current age be $s$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $s = 2u$ 42 years ago, Stephanie was $s - 42$ years old, and Umaima was $u - 42$ years old. The information in the second sentence can be expressed in the following equation: $s - 42 = 9(u - 42)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $s$ and substitute it into our second equation. Our first equation is: $s = 2u$ . Substituting this into our second equation, we get: $2u$ $-$ $42 = 9(u - 42)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $2 u - 42 = 9 u - 378$ Solving for $u$ , we get: $7 u = 336.$ $u = 48$.